456 



THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956 



the figure are for random (Poisson) traffic having the same mean values 

 as the /'' distributions. The negative binomial provides excellent fits 

 down to cumulated probabilities of 0.01, with a tendency thereafter to 

 give somewhat larger values than the true ones. The Poisson agreement 

 is good only for the overflow from a single trunk, as might have been 

 anticipated, the divergence rapidly increasing thereafter. 



Fig. 15 corresponds with the cases of Fig. 14 except that the true over- 

 flow Fxi^n) distributions for the conditional situation of all .r-paths 

 busy, are fitted. Again the negative binomial is seen to give a good agree- 

 ment down to 0.01 probability, with somewhat too-high estimates for 

 larger values of the simultaneous overflow calls n. 



Fig. 16 shows additional comparisons of overflow and negative bi- 

 nomial distributions. As before, the agreement is quite satisfactory to 

 0.01 probability, the negative binomial thereafter tending to give some- 

 what high values. 



On Fig. 17 are compared the individual 6(n) density distributions for 

 several cases. The agreement of the negative binomial with the true 

 distribution is seen to be uniformly good. The dots indicate the random 

 (Poisson) individual term distribution corresponding to the a = 9.6 case- 



t 2 3 4 5 6 7 8 9 10 11 12 13 14 15 

 n = NUMBER OF SIMULTANEOUS CALLS 



Fig. 14 — Probability distributions of overflow traffic with 5 erlangs offered to 

 1, 2, 5, and 10 trunks, fitted by negative binomial. 



I 



